The present invention generally relates to forming of images and more particularly to an image forming apparatus wherein a sequential image data supplied thereto is expanded into a bit image and stored sequentially in a memory device, and wherein, when all the bit images are stored, the bit images are read out from the memory device for printing.
In an image forming apparatus of the type called a page printer or a laser printer, graphic images or large size letters can be printed on a sheet with high quality as a result of use of the page describe language. However, the process, performed by the page describe language, for calculating the coordinate of the bit images on the sheet involves a complex calculation and there is a problem that such an image forming apparatus requires a substantial time for such a processing.
FIGS. 1A and 1B show an example of the process performed using such a page describe language. According to this process, a curve image is represented by a so-called Bezier curve in which the shape and size of the curve image are determined by specifying the position of four points on the curve, two of which being at the end of the curve as represented by a point A and a point B, and the other two of which are control points C1 and C2 located on the tangentials of the curve image drawn at the respective ends of the curve image.
In the actual process, line segments connecting the point A and the point C1, the point C1 and the point C2, the point C2 and the point B, are calculated and the center of these line segments are obtained as mid-points AC1, C1C2 and C2B. Further, by connecting these mid-points AC1, C1C2 and C2B, an approximation of the original curve is obtained. By repeating the foregoing processes for a number of times, an increasingly improved approximation of the original image is obtained as illustrated in FIG. 1B.
The actual calculation is performed as follows. Assuming that a third order Bezier curve is used, the x- and y-coordinates of the points on the curve are represented, using a parameter t, (0&lt;t&lt;1) as follows: EQU x(t)=a.sub.x .multidot.t.sup.3 +b.sub.x .multidot.t.sup.2 +c.sub.x .multidot.t+x.sub.0 EQU y(t)=a.sub.y .multidot.t.sup.3 +b.sub.y .multidot.t.sup.2 +c.sub.y .multidot.t+y.sub.0
where the parameter t is changed from 0 to 1, and the coefficients are defined as EQU c.sub.x =3(x.sub.0 -x.sub.1),c.sub.y =3(y.sub.1 -y.sub.0) EQU b.sub.x =3(x.sub.2 -2x.sub.1 +x.sub.0) EQU b.sub.y =3(y.sub.2 -2y.sub.1 +y.sub.0) EQU a.sub.x =x.sub.3 -x.sub.0 +3(-x.sub.2 +x.sub.1) EQU a.sub.y =y.sub.3 -y.sub.0 +3(-y.sub.2 +y.sub.1)
in which x.sub.0 and y.sub.0 are the coordinates of the first end point A, x.sub.1 and y.sub.1 are the coordinates of the first control point Cl, x.sub.2 and y.sub.2 are the coordinates of the second control point point C2, and x.sub.3 and y.sub.3 are the coordinates of the second end point B.
By changing the parameter t between zero and one with an identical interval, the approximation of the curve is obtained by the foregoing equation. Thereby, by increasing the number of divisions in the interval of the parameter t, the smoothness of the reproduced curve is improved. However, such an increase of the number of divisions inevitably invites increased number of calculations which in turn invites the increase of processing time.
When the foregoing process is applied to the image forming apparatus of the page printer type such as the laser printer, it will be understood that a considerable time is needed for the foregoing processing, and during the processing, the image forming apparatus cannot perform the printing. Thus, the user of the image forming apparatus has to wait before the apparatus starts printing until the foregoing processing is completed, without knowing when such a processing will end.